Strong base for fuzzy topology

Abstract

It is known that a base for a traditional topology, or for a $L$-topology, $\tau$, is a subset ${\mathcal B}$ of $\tau$ with the property that every element $G\in \tau$ can be written as a union of elements of ${\mathcal B}$. In the classical case it is equivalent to say that $G\in \tau$ if and only if for any $x\in G$ we have $B\in {\mathcal B}$ satisfying $x\in B \subseteq G$. This latter property is taken as the foundation for a notion of strong base for a $L$-topology. Characteristic properties of a strong base are given and among other results it is shown that a strong base is a base, but not conversely.

Full Text

Article Information

Title	Strong base for fuzzy topology
Source	Methods Funct. Anal. Topology, Vol. 17 (2011), no. 4, 350-355
MathSciNet	MR2907363
Copyright	The Author(s) 2011 (CC BY-SA)

Authors Information

A. A. Rakhimov
Tashkent Institute of Railways and Engineering, Tashkent, Uzbekistan; Karadeniz Technical University, Turkey

F. M. Zakirov
Tashkent Autoroad Institute, Tashkent, Uzbekistan 

Citation Example

A. A. Rakhimov and F. M. Zakirov, Strong base for fuzzy topology, Methods Funct. Anal. Topology 17 (2011), no. 4, 350-355.

BibTex

@article {MFAT582,
    AUTHOR = {Rakhimov, A. A. and Zakirov, F. M.},
     TITLE = {Strong base for fuzzy topology},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {17},
      YEAR = {2011},
    NUMBER = {4},
     PAGES = {350-355},
      ISSN = {1029-3531},
  MRNUMBER = {MR2907363},
       URL = {https://mfat.imath.kiev.ua/article/?id=582},
}